Renormalization and conformal invariance of non-local quantum electrodynamics

Heydeman, Matthew; Jepsen, Christian Baadsgaard; Ji, Ziming; Yarom, Amos

doi:10.1007/jhep08(2020)007

Cited by 20 publications

(18 citation statements)

References 85 publications

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“…A more careful argument shows that the same is true for marginally relevant deformations[42] 13. See[51,52] for recent discussions of the optical theorem for boundary field theories (and more general nonlocal field theories).…”

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confidence: 88%

Defect a-theorem and a-maximization

Wang

2022

J. High Energ. Phys.

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Conformal defects describe the universal behaviors of a conformal field theory (CFT) in the presence of a boundary or more general impurities. The coupled critical system is characterized by new conformal anomalies which are analogous to, and generalize those of standalone CFTs. Here we study the conformal a- and c-anomalies of four dimensional defects in CFTs of general spacetime dimensions greater than four. We prove that under unitary defect renormalization group (RG) flows, the defect a-anomaly must decrease, thus establishing the defect a-theorem. For conformal defects preserving minimal supersymmetry, the full defect symmetry contains a distinguished U(1)R subgroup. We derive the anomaly multiplet relations that express the defect a- and c-anomalies in terms of the defect (mixed) ’t Hooft anomalies for this U(1)R symmetry. Once the U(1)R symmetry is identified using the defect a-maximization principle which we prove, this enables a non-perturbative pathway to the conformal anomalies of strongly coupled defects. We illustrate our methods by discussing a number of examples including boundaries in five dimensions and codimension-two defects in six dimensions. We also comment on chiral algebra sectors of defect operator algebras and potential conformal collider bounds on defect anomalies.

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confidence: 88%

Defect a-theorem and a-maximization

Wang

2022

J. High Energ. Phys.

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“…By varying the full action S + S Σ with respect to Φ, we see the boundary condition gets 13 See [51,52] for recent discussions of the optical theorem for boundary field theories (and more general nonlocal field theories).…”

Section: Explicit Boundary Rg Flow In the Free Scalar Theorymentioning

confidence: 99%

Defect $a$-Theorem and $a$-Maximization

Wang

2021

Preprint

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Conformal defects describe the universal behaviors of a conformal field theory (CFT) in the presence of a boundary or more general impurities. The coupled critical system is characterized by new conformal anomalies which are analogous to, and generalize those of standalone CFTs. Here we study the conformal a-and c-anomalies of four dimensional defects in CFTs of general spacetime dimensions greater than four. We prove that under unitary defect renormalization group (RG) flows, the defect a-anomaly must decrease, thus establishing the defect a-theorem. For conformal defects preserving minimal supersymmetry, the full defect symmetry contains a distinguished U (1) R subgroup. We derive the anomaly multiplet relations that express the defect a-and c-anomalies in terms of the defect (mixed) 't Hooft anomalies for this U (1) R symmetry. Once the U (1) R symmetry is identified using the defect a-maximization principle which we prove, this enables a non-perturbative pathway to the conformal anomalies of strongly coupled defects. We illustrate our methods by discussing a number of examples including boundaries in five dimensions and codimension-two defects in six dimensions. We also comment on chiral algebra sectors of defect operator algebras and potential conformal collider bounds on defect anomalies.

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“…In section 5, we looked at a q = 2 and q = 3 "wedge" theory as a prelude to looking at higher codimension theories with charged matter on the defect. Literature suggests that the q = 2 theory with charged matter on the defect is problematic [22,23] because the effective photon propagator experienced by the matter has a logarithm in it and requires a scale to be well defined. We would like to explore what happens in dimensional regularization, moving slightly away from the q = 2 limit whether conformal defect constraints can be applied.…”

Section: Jhep04(2021)226mentioning

confidence: 99%

Two point functions in defect CFTs

Herzog

Shrestha

2021

J. High Energ. Phys.

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This paper is designed to be a practical tool for constructing and investigating two-point correlation functions in defect conformal field theory, directly in physical space, between any two bulk primaries or between a bulk primary and a defect primary, with arbitrary spin. Although geometrically elegant and ultimately a more powerful approach, the embedding space formalism gets rather cumbersome when dealing with mixed symmetry tensors, especially in the projection to physical space. The results in this paper provide an alternative method for studying two-point correlation functions for a generic d-dimensional conformal field theory with a flat p-dimensional defect and d − p = q co-dimensions. We tabulate some examples of correlation functions involving a conserved current, an energy momentum tensor and a Maxwell field strength, while analysing the constraints arising from conservation and the equations of motion. A method for obtaining bulk-to-defect correlators is also explained. Some explicit examples are considered: free scalar theory on ℝp× (ℝq/ℤ2) and a free four dimensional Maxwell theory on a wedge.

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Renormalization and conformal invariance of non-local quantum electrodynamics

Cited by 20 publications

References 85 publications

Defect a-theorem and a-maximization

Defect a-theorem and a-maximization

Defect $a$-Theorem and $a$-Maximization

Two point functions in defect CFTs

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